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(3x^2)*(e^-x^3)
Solving integrals/ (3x^2)*(e^-x^3)

Integral of (3x^2)*(e^-x^3) dx

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The solution

You have entered [src] 
 oo             
  /             
 |              
 |          3   
 |     2  -x    
 |  3*x *e    dx
 |              
/               
2
∫2∞3x2e−x3 dx\int\limits_{2}^{\infty} 3 x^{2} e^{- x^{3}}\, dx 
Integral(3*x^2/E^(x^3), (x, 2, oo))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫3x2e−x3 dx=3∫x2e−x3 dx\int 3 x^{2} e^{- x^{3}}\, dx = 3 \int x^{2} e^{- x^{3}}\, dx

    1. Let u=e−x3u = e^{- x^{3}}.

      Then let du=−3x2e−x3dxdu = - 3 x^{2} e^{- x^{3}} dx and substitute −du3- \frac{du}{3}:

      ∫19 du\int \frac{1}{9}\, du

      1. The integral of a constant times a function is the constant times the integral of the function:

        ∫(−13) du=−∫1 du3\int \left(- \frac{1}{3}\right)\, du = - \frac{\int 1\, du}{3}

        1. The integral of a constant is the constant times the variable of integration:

          ∫1 du=u\int 1\, du = u

        So, the result is: −u3- \frac{u}{3}

      Now substitute uu back in:

      −e−x33- \frac{e^{- x^{3}}}{3}

    So, the result is: −e−x3- e^{- x^{3}}

  2. Add the constant of integration:

    −e−x3+constant- e^{- x^{3}}+ \mathrm{constant}

The answer is:

−e−x3+constant- e^{- x^{3}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                       
 |                        
 |         3             3
 |    2  -x            -x 
 | 3*x *e    dx = C - e   
 |                        
/
−e−x3-e^ {- x^3 }
Simplify
The graph
2.00002.01002.00102.00202.00302.00402.00502.00602.00702.00802.00900.005-0.005
Plot the graph f(x)
The answer [src] 
 -8
e
3 (e−83−e−oo33)3\,\left({{e^ {- 8 }}\over{3}}-{{e^ {- {\it oo}^3 }}\over{3}} \right) 
=
= 
 -8
e
e−8e^{-8}
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The graph
Integral of (3x^2)*(e^-x^3) dx

    Use the examples entering the upper and lower limits of integration.

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